The causes of a wobbly toilet are pretty straightforward; either the closet bolts are loose or the wax ring is failing. Fixing either of these issues is also pretty straightforward:
1.. Remove the bolt covers and try to turn the bolts by hand. If the bolts are loose, tighten them carefully with a wrench to avoid cracking the porcelain.
2. Turn off the water to the toilet and hold down the handle until all the water drains away.
3. If the bolts are tight, remove them and find a helper to lift the toilet off the wax ring and flange. Remove the bolts from the flange, and scrape the existing wax ring off and check the condition of the flange. If the flange is in good shape*, use two new wax rings, one on top of the other, and replace the closet bolts.
4. Re-position the toilet and shimmy it back into place, then tighten the closet bolts again.
*If the flange is damaged – bent or broken on only one side – a flange repair kit should solve the problem. A licensed plumber should be called, though, if both sides of the flange are damaged.